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Tensor Rank and Complexity
Zitatschlüssel	OR-TensorRankAndComplexity
Autor	Giorgio Ottaviani and Philipp Reichenbach
Jahr	2020
Monat	4
Zusammenfassung	These lecture notes are intended as an introduction to several notions of tensor rank and their connections to the asymptotic complexity of matrix multiplication. The latter is studied with the exponent of matrix multiplication, which will be expressed in terms of tensor (border) rank, (border) symmetric rank and the asymptotic rank of certain tensors. We introduce the multilinear rank of a tensor as well, deal with the concept of tensor equivalence and study prehomogeneous vector spaces with the Castling transform. Moreover, we treat Apolarity Theory and use it to determine the symmetric rank (Waring rank) of some symmetric tensors.

Link zur Publikation [1] Download Bibtex Eintrag [2]

Zurück [3]

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[1] https://arxiv.org/abs/2004.01492

[2] https://www.math.tu-berlin.de/fachgebiete_ag_diskal
g/fachgebiet_algorithmische_algebra/v_menue/publication
s/preprints/parameter/maxhilfe/?no_cache=1&tx_sibib
tex_pi1%5Bdownload_bibtex_uid%5D=6201813&tx_sibibte
x_pi1%5Bcontentelement%5D=tt_content%3A541953

[3] https://www.math.tu-berlin.de/fachgebiete_ag_diskal
g/fachgebiet_algorithmische_algebra/v_menue/publication
s/preprints/parameter/maxhilfe/